Question

If G be the geometric mean of x and y, then $\frac{1}{G^2-x^2}+\frac{1}{G^2-y^2}=$

• A. G²
• B.
• C.
• D. 3G²

Answer 1

The correct option is B

As given, $G=\sqrt{xy}$
$\therefore \frac{1}{G^2-x^2}+\frac{1}{G^2-y^2}=\frac{1}{xy-x^2}+\frac{1}{xy-y^2}$
$=\frac{1}{x-y}\{-\frac{1}{x}+\frac{1}{y}\}=\frac{1}{xy}=\frac{1}{G^2}$
Trick : $x=1,G=2,y=4$